To find the value of (x+6)(x+6) = 256, you first need to simplify the left hand side of the equation:
(x+6)(x+6) = x2 +6x +6x + 36 = x2 + 12x + 36
Substituting this to the original equation will give you this x2 + 12x + 36 = 256, which can further be simplified by moving all terms to the left. Doing that will give you the quadratic form (ax2 + b2 + c = 0) of the equation:
x2 + 12x - 220 = 0
Remember that the roots can be obtained by using the quadratic formula given by:
x = [(-b)±√b2-(4ac)] / 2a where a, b, c are the coefficients of the equation. That is, a = 1, b = 12 and c = -220
Substituting the values will give you:
x = [-(12)±√(12)2-(4*1*-220)] / 2(1)
x = [-12±√144-(-880)] / 2
x = [-12±√1024] / 2
x = [-12±32] / 2
First root now equals to:
x = [-12+32] / 2
x = 10
Second root:
x = [-12-32] / 2
x = -22
There you have it. The values of x are 10 and -22.
(x + 6)(x + 6) = x(x + 6) + 6(x + 6) = x^2 + 12x + 36
Now we can substitute this expression into the original equation:
x^2 + 12x + 36 = 256
Subtracting 256 from both sides, we get:
x^2 + 12x - 220 = 0
To solve for x, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 12, and c = -220. Substituting these values into the formula, we get:
x = (-12 ± sqrt(12^2 - 4(1)(-220))) / 2(1)
Simplifying, we get:
x = (-12 ± sqrt(144 + 880)) / 2
x = (-12 ± sqrt(1024)) / 2
x = (-12 ± 32) / 2
Therefore, the solutions for x are:
x = (-12 + 32) / 2 = 10